Informed sub-sampling MCMC: approximate Bayesian inference for large datasets

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Title: Informed sub-sampling MCMC: approximate Bayesian inference for large datasets
Authors: Maire, Florian
Friel, Nial
Alquier, Pierre
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Date: 9-Jun-2018
Online since: 2019-05-13T09:14:31Z
Abstract: This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an unknown fraction of fixed size of the available data that is randomly refreshed throughout the algorithm. Inspired by the Approximate Bayesian Computation literature, the subsampling process is guided by the fidelity to the observed data, as measured by summary statistics. The resulting algorithm, Informed Sub-Sampling MCMC, is a generic and flexible approach which, contrary to existing scalable methodologies, preserves the simplicity of the Metropolis–Hastings algorithm. Even though exactness is lost, i.e the chain distribution approximates the posterior, we study and quantify theoretically this bias and show on a diverse set of examples that it yields excellent performances when the computational budget is limited. If available and cheap to compute, we show that setting the summary statistics as the maximum likelihood estimator is supported by theoretical arguments.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Springer
Journal: Statistics and Computing
Volume: 29
Issue: 3
Start page: 449
End page: 482
Copyright (published version): 2018 Springer
Keywords: Bayesian inferenceBig-dataApproximate Bayesian computationNoisy Markov chain Monte Carlo
DOI: 10.1007/s11222-018-9817-3
Language: en
Status of Item: Peer reviewed
Appears in Collections:Insight Research Collection

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